No one here is arguing on behalf of "twinkle", no one is as invested in the term as you seem to be. Chances are you've given more thought and time to the whole thing than anyone else here. The term is not something definitive and no one is trying to pass it off as that, it's (along with most sub-genres) a simple way of describing a certain sound. At this point using the term emo is too broad, and I sure as hell will not write a detailed description of the sound every time I wanna talk about a band like that. Sub-genres are a quick way of describing a band in hopes that most people will understand what you're talking about without having to get too into detail.

In short the only person giving importance to the term is you, and you're using a dumb and generalizing argument to support yourself.